Symmetric and Geometric Methods

对称和几何方法

• 批准号: 9554850
• 负责人: Amir Assadi
• 金额: $ 2.52万
• 依托单位: University of Wisconsin-Madison
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1996
• 资助国家: 美国
• 起止时间: 1996-01-01 至 1997-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9554850&HistoricalAwards=false
• 关键词: Symmetric; Geometric; Methods

Symmetry has played a ubiquitous role in our civilization throughout all ages. Mankind has been fascinated by the inherent beauty of symmetry in nature and has explored and searched for understanding its implications in his culture. This preoccupation with symmetry has led to discovery of rich mathematical theories to explain and apply symmetry in a vast number of subjects ranging from anthropology and the arts to engineering and the sciences. This project proposes to use symmetry and geometric methods in the sciences, the arts and engineering as a theme to develop topic-oriented course-modules that can be adapted in revitalizing undergraduate education in mathematics and other subjects. It is proposed to expose and explore some of these theories in their context of discovery and applications, constantly drawing attention to the quantitative and qualitative geometric methods that accompany the intuitive reasoning. It is reasonable to expect that a number of students will be attracted to engineering, mathematics and the sciences through their experience with such material. The proposed lab portion of the course-modules intends to get the students involved hands-on in exploring modern and advanced topics that are inaccessible in the present linearly ordered college curriculum, especially those that requires prerequisites from several mathematics and science courses.

对称性在我们的文明中一直扮演着无处不在的角色。 人类一直着迷于自然界中固有的对称美，并探索和寻求理解其在文化中的含义。这种对对称性的关注导致了丰富的数学理论的发现，这些理论可以解释对称性并将其应用于从人类学和艺术到工程和科学的大量学科中。 该项目建议在科学、艺术和工程学中使用对称和几何方法作为主题，以开发面向主题的课程模块，这些模块可用于振兴数学和其他学科的本科教育。 建议对其中的一些理论进行揭露和探讨 在 他们的发现和应用的背景下，不断提请注意定量和定性几何方法，伴随着直观的推理。 可以合理地预期，一些学生将通过他们对这些材料的经验而被吸引到工程、数学和科学领域。 课程模块的拟议实验室部分旨在让学生参与实践探索现代和先进的主题，这些主题在目前线性有序的大学课程中无法访问，特别是那些需要几门数学和科学课程的先决条件的主题。